Let Find fof.

Let f be a real function given by . Find each of the following:

(fofof)(38)

Let f be a real function given by . Find each of the following:

f²

Also, show that fof ≠ f².

If f, g: R → R be two functions defined as f(x) = |x| + x and

g(x) = |x|–x for all x ∈ R. Then, find fog and gof. Hence, find fog (–3),

fog (5) and gof(–2).

State with reasons whether the following functions have inverse:

(i) f : [1, 2, 3, 4] → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}

(ii) g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}

(iii) h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}